The best way would be to write your code in the version 13 CMS as a scheduled task AFTER you have all your pages type definitions in the new CMS. Query the old CMS using the view view_cms_tree_joimed
which will get you all the node, document, and type of page it is. Then create a recursive method to insert the documents based on nodeid and nodeparentid into your content tree.
This would not get you any page type fields but it could if you worry more code to handle each page type. It sounds easy but will be a daunting task. I'd only suggest going down this road I'd you have budget and thousands of pages. Speaking from experience, with just a basic structure you could copy and paste even 500 pages faster than you could write, test and execute code to transfer those same 500 pages.